Magnetophonon spectroscopy of Dirac fermion scattering by transverse and longitudinal acoustic phonons in graphene

M T Greenaway,L Eaves,R Krishna Kumar,A K Geim,P Kumaravadivel

doi:10.1103/physrevb.100.155120

Abstract

Recently observed magnetophonon resonances in the magnetoresistance of graphene are investigated using the Kubo formalism. This analysis provides a quantitative fit to the experimental data over a wide range of carrier densities. It demonstrates the predominance of carrier scattering by low energy transverse acoustic (TA) mode phonons: the magnetophonon resonance amplitude is significantly stronger for the TA modes than for the longitudinal acoustic (LA) modes. We demonstrate that the LA and TA phonon speeds and the electron-phonon coupling strengths determined from the magnetophonon resonance measurements also provide an excellent fit to the measured dependence of the resistivity at zero magnetic field over a temperature range of 4-150 K. A semiclassical description of magnetophonon resonance in graphene is shown to provide a simple physical explanation for the dependence of the magneto-oscillation period on carrier density. The correspondence between the quantum calculation and the semiclassical model is discussed.

Highlights

In 1961, theoretical work by Gurevich and Firsov predicted that inelastic scattering of electrons by phonons can induce oscillations in the magnetoresistance of semiconductors [1]
Observed magnetophonon resonances in the magnetoresistance of graphene are investigated using the Kubo formalism. This analysis provides a quantitative fit to the magnetophonon resonances over a wide range of carrier densities. It demonstrates the predominance of carrier scattering by low-energy transverse acoustic (TA) mode phonons: the magnetophonon resonance amplitude is significantly stronger for the TA modes than for the longitudinal acoustic (LA) modes
We demonstrate that the LA and TA phonon speeds and the electron-phonon coupling strengths determined from the magnetophonon resonance measurements provide an excellent fit to the measured dependence of the resistivity at zero magnetic field over a temperature range of 4–150 K

Summary

INTRODUCTION

In 1961, theoretical work by Gurevich and Firsov predicted that inelastic scattering of electrons by phonons can induce oscillations in the magnetoresistance of semiconductors [1]. Absorption or emission of a phonon can induce a shift of the electron’s cyclotron orbit center This causes it to drift in the presence of an applied voltage and give rise to an enhancement of the magnetoconductance when the resonant condition is satisfied. The result is a series of oscillations in the magnetoconductance that are observable over a wide range of temperatures, are periodic in inverse magnetic field, and are independent of carrier density. A different type of MPR was observed at low temperatures in the magnetoresistance of a modulation doped (AlGa)AsGaAs heterostructure [8,9,10]. Under these conditions MPR was shown to arise from scattering of the two-dimensionally. We demonstrate how electrical screening of the deformation potential accounts, in part, for the smaller amplitude of the LA phonon resonances

SEMICLASSICAL ANALYSIS

QUANTUM CALCULATION OF ρyy

DISCUSSION

TEMPERATURE DEPENDENCE OF RESISTIVITY IN THE ABSENCE OF A MAGNETIC FIELD

CONCLUSIONS